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SUMMARY:Nicolas Gilliers (University of Toulouse)
DTSTART:20211008T130000Z
DTEND:20211008T140000Z
DTSTAMP:20260423T021652Z
UID:ACPMS/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ACPMS/13/">B
 inary trees\, operads and Dykema’s T-transform in Free Probability</a>\n
 by Nicolas Gilliers (University of Toulouse) as part of Algebraic and Comb
 inatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nIn this
  talk\, we shall discuss an operadic perspective on K. Dykema’s twisted 
 factorization formula for the operator-valued T-transform in free probabil
 ity. To begin with\, we introduce in the general setting of an operad with
  multiplication two group products on formal series of operators\, besides
  the one introduced by F. Chapoton. We explain how those products relate b
 y means of certain transformation\, that we call (abstract) T-transform\, 
 borrowing terminology from free probability. Specializing in the endomorph
 ism operad gives a new perspective on the twisted factorization of the T-t
 ransform and to multiplicative free convolution. We will discuss connectio
 ns to the work of A. Frabetti and C. Brouder by specializing our construct
 ion to the duoidal and dendriform operads.\n
LOCATION:https://researchseminars.org/talk/ACPMS/13/
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